A Quantum Computational Semantics for Epistemic Logical Operators. Part II: Semantics |
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Authors: | Enrico Beltrametti Maria Luisa Dalla Chiara Roberto Giuntini Roberto Leporini Giuseppe Sergioli |
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Institution: | 1. Dipartimento di Fisica, Università di Genova, Via Dodecaneso, 33, 16146, Genova, Italy 2. Dipartimento di Filosofia, Università di Firenze, Via Bolognese 52, 50139, Firenze, Italy 3. Dipartimento di Filosofia e Teoria delle Scienze Umane, Università di Cagliari, Via Is Mirrionis 1, 09123, Cagliari, Italy 4. Dipartimento di Ingegneria, Università di Bergamo, viale Marconi 5, 24044, Dalmine, BG, Italy
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Abstract: | By using the abstract structures investigated in the first Part of this article, we develop a semantics for an epistemic language, which expresses sentences like “Alice knows that Bob does not understand that π is irrational”. One is dealing with a holistic form of quantum computational semantics, where entanglement plays a fundamental role; thus, the meaning of a global expression determines the contextual meanings of its parts, but generally not the other way around. The epistemic situations represented in this semantics seem to reflect some characteristic limitations of the real processes of acquiring information. Since knowledge is not generally closed under logical consequence, the unpleasant phenomenon of logical omniscience is here avoided. |
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